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**Impact Evaluation Methods: Causal Inference**

Sebastian Martinez Impact Evaluation Cluster, AFTRL Slides by Paul J. Gertler & Sebastian Martinez

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**Motivation “Traditional” M&E:**

Is the program being implemented as designed? Could the operations be more efficient? Are the benefits getting to those intended? Monitoring trends Are indicators moving in the right direction? NO inherent Causality Impact Evaluation: What was the effect of the program on outcomes? Because of the program, are people better off? What would happen if we changed the program? Causality

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**Policy Intervention Monitoring Impact Evaluation**

Increase Access and Quality in Early Child Education Construction Feeding Quality -New classrooms -SES of students # of Meals Use of curriculum -Increased attendance health/growth Cognitive Development Improve learning in Science and Math in high school Upgrade science laboratories Training of instructors - # equipped labs # trained instructors Lab attendance & use Learning Labor market University enrollment Need at least 10 people who would be willing to volunteer {to answer some type of question} Everyone else – randomly draw survey form and fill it out – anonymous Answers are secret and anonymous - don’t show your answer to your neighbors! (and don’t look at your neighbor) Improve quality of instruction in higher education Teacher training Online courses # of training sessions # of internet terminals Learning Attendance/drop out Labor market

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Motivation Objective in evaluation is to estimate the CAUSAL effect of intervention X on outcome Y What is the effect of a cash transfer on household consumption? For causal inference we must understand the data generation process For impact evaluation, this means understanding the behavioral process that generates the data how benefits are assigned

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**Causation versus Correlation**

Recall: correlation is NOT causation Necessary but not sufficient condition Correlation: X and Y are related Change in X is related to a change in Y And…. A change in Y is related to a change in X Causation – if we change X how much does Y change A change in X is related to a change in Y Not necessarily the other way around

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**Causation versus Correlation**

Three criteria for causation: Independent variable precedes the dependent variable. Independent variable is related to the dependent variable. There are no third variables that could explain why the independent variable is related to the dependent variable External validity Generalizability: causal inference to generalize outside the sample population or setting

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Motivation The word cause is not in the vocabulary of standard probability theory. Probability theory: two events are mutually correlated, or dependent if we find one, we can expect to encounter the other. Example age and income For impact evaluation, we supplement the language of probability with a vocabulary for causality.

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**Statistical Analysis & Impact Evaluation**

Statistical analysis: Typically involves inferring the causal relationship between X and Y from observational data Many challenges & complex statistics Impact Evaluation: Retrospectively: same challenges as statistical analysis Prospectively: we generate the data ourselves through the program’s design evaluation design makes things much easier!

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How to assess impact What is the effect of a cash transfer on household consumption? Formally, program impact is: α = (Y | P=1) - (Y | P=0) Compare same individual with & without programs at same point in time So what’s the Problem?

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**Solving the evaluation problem**

Problem: we never observe the same individual with and without program at same point in time Need to estimate what would have happened to the beneficiary if he or she had not received benefits Counterfactual: what would have happened without the program Difference between treated observation and counterfactual is the estimated impact

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**Estimate effect of X on Y**

Compare same individual with & without treatment at same point in time (counterfactual): Program impact is outcome with program minus outcome without program sick 2 days sick 10 days Impact = = - 8 days sick!

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**Finding a good counterfactual**

The treated observation and the counterfactual: have identical factors/characteristics, except for benefiting from the intervention No other explanations for differences in outcomes between the treated observation and counterfactual The only reason for the difference in outcomes is due to the intervention

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**Measuring Impact Tool belt of Impact Evaluation Design Options:**

Randomized Experiments Quasi-experiments Regression Discontinuity Difference in difference – panel data Other (using Instrumental Variables, matching, etc) In all cases, these will involve knowing the rule for assigning treatment

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Choosing your design For impact evaluation, we will identify the “best” possible design given the operational context Best possible design is the one that has the fewest risks for contamination Omitted Variables (biased estimates) Selection (results not generalizable)

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**Case Study Effect of cash transfers on consumption**

Estimate impact of cash transfer on consumption per capita Make sure: Cash transfer comes before change in consumption Cash transfer is correlated with consumption Cash transfer is the only thing changing consumption Example based on Oportunidades

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**Oportunidades National anti-poverty program in Mexico (1997)**

Cash transfers and in-kind benefits conditional on school attendance and health care visits. Transfer given preferably to mother of beneficiary children. Large program with large transfers: 5 million beneficiary households in 2004 Large transfers, capped at: $95 USD for HH with children through junior high $159 USD for HH with children in high school

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**Oportunidades Evaluation**

Phasing in of intervention 50,000 eligible rural communities Random sample of of 506 eligible communities in 7 states - evaluation sample Random assignment of benefits by community: 320 treatment communities (14,446 households) First transfers distributed April 1998 186 control communities (9,630 households) First transfers November 1999

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**Oportunidades Example**

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**Common Counterfeit Counterfactuals**

2005 2007 1. Before and After: 2. Enrolled / Not Enrolled: Sick 2 days Sick 15 days Impact = = 13 more days sick? Sick 2 days Sick 1 day Impact = = + 1 day sick?

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**“Counterfeit” Counterfactual Number 1**

Before and after: Assume we have data on Treatment households before the cash transfer Treatment households after the cash transfer Estimate “impact” of cash transfer on household consumption: Compare consumption per capita before the intervention to consumption per capita after the intervention Difference in consumption per capita between the two periods is “treatment”

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**Case 1: Before and After Compare Y before and after intervention**

αi = (CPCit | T=1) - (CPCi,t-1| T=0) Estimate of counterfactual (CPCi,t| T=0) = (CPCi,t-1| T=0) “Impact” = A-B CPC Before After A B t-1 t Time

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**Case 1: Before and After 35.27** 34.28** Control - Before**

Treatment - After t-stat Mean 233.48 268.75 16.3 Case 1 - Before and After Linear Regression Multivariate Linear Regression Estimated Impact on CPC 35.27** 34.28** (2.16) (2.11) ** Significant at 1% level Case 1 - Before and After

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**Case 1: Before and After Compare Y before and after intervention**

αi = (CPCit | T=1) - (CPCi,t-1| T=0) Estimate of counterfactual (CPCi,t| T=0) = (CPCi,t-1| T=0) “Impact” = A-B Does not control for time varying factors Recession: Impact = A-C Boom: Impact = A-D CPC Before After A D? B C? t-1 t Time

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**“Counterfeit” Counterfactual Number 2**

Enrolled/Not Enrolled Voluntary Inscription to the program Assume we have a cross-section of post-intervention data on: Households that did not enroll Households that enrolled Estimate “impact” of cash transfer on household consumption: Compare consumption per capita of those who did not enroll to consumption per capita of those who enrolled Difference in consumption per capita between the two groups is “treatment”

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**Case 2: Enrolled/Not Enrolled**

t-stat Mean CPC 290.16 5.6 Case 2 - Enrolled/Not Enrolled Linear Regression Multivariate Linear Regression Estimated Impact on CPC -22.7** -4.15 (3.78) (4.05) ** Significant at 1% level Case 2 - Enrolled/Not Enrolled

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**Those who did not enroll….**

Impact estimate: αi = (Yit | P=1) - (Yj,t| P=0) , Counterfactual: (Yj,t| P=0) ≠ (Yi,t| P=0) Examples: Those who choose not to enroll in program Those who were not offered the program Conditional Cash Transfer Job Training program Cannot control for all reasons why some choose to sign up & other didn’t Reasons could be correlated with outcomes We can control for observables….. But are still left with the unobservables

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**Impact Evaluation Example: Two counterfeit counterfactuals**

What is going on?? Which of these do we believe? Problem with Before-After: Can not control for other time-varying factors Problem with Enrolled-Not Enrolled: Do no know why the treated are treated and the others not Linear Regression Multivariate Linear Estimated Impact on CPC 35.27** 34.28** -22.7** -4.15 (2.16) (2.11) (3.78) (4.05) ** Significant at 1% level Case 1 - Before and After Case 2 - Enrolled/Not Enrolled

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**Solution to the Counterfeit Counterfactual**

Sick 2 days Sick 10 days Observe Y with treatment ESTIMATE Y without treatment Impact = = - 8 days sick! On AVERAGE, is a good counterfactual for

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**Possible Solutions… We need to understand the data generation process**

How beneficiaries are selected and how benefits are assigned Guarantee comparability of treatment and control groups, so ONLY difference is the intervention

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**Measuring Impact Experimental design/randomization Quasi-experiments**

Regression Discontinuity Double differences (diff in diff) Other options

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